According to Sidney Greenbaum and Randolph Quirk, adverbial clauses function mainly as adjuncts or disjuncts. In those functions they are like adverbial phrases, but in their potentiality for greater explicitness, they are more often like prepositional phrases (Greenbaum and Quirk,1990):

We left after the speeches ended. (Is it an adverbial clause, adverbial phrase or preposition phrase?)

We left after the end of the speeches.(Is it an adverbial clause, adverbial phrase or preposition phrase?)